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Full text of "Jet diffusion in proximity of a wall"

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NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 



TECHNICAL MEMORANDUM 

No. 1214 



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JET DIFFUSION IN PROXIMITY OF A WALL 
By D. Kiichemann 



Translation of ZWB Untersuchungen und Mitteilungen Nr. 3057, 

December 1943 




Washington 
May 1949 



I2^HH ifO 



N-ATIONAL ADVISORY COMMITTTHE FOE AERONAUTICS 



TECHi^rICAI■ MEMOPAffiDUM NO. 121^1 



JET DI&TBTJBION IN PROXBIETY OF A W.Jlt 
3y D. IZucIiomarm 

SIM'IARY 



Wlien au:;iliary ^ct ensines are instelled on airframes, as 
■(•rell aa in somo neir designs, the jet ensinop. ai.-e mounted in aiich 
a way that the jet strsaci exhausts in close proximity to the 
fuselage. This report deals with the behavior of the jet in 
close proximity to a two-dimensional surface. The ezpei-iments 
were made to find out vrhether the axially symmotric stroem tends 
to approach the flat Burfaco. This report is the last of a seiles 
of fovr partial teat reports of the G-Sttingen progr-Mi for 
the installation of jet engines, dated Octoher 12, 19^+3 • -his report 
is the complement of the report on intake in close proximity to 
a wcJ-l. 



I. IKIRODUCTIon 



Considerahle confusion sti!)JL attends the installEtion of turbojet 
engines as regards the dischar-ging jot, especiallj^ when it comes 
near other parts of the airplane and interference phenomena a:!:'e 
possible. If the engine is mounted near to the fuselage, there is 
apprehension that the jot will adhex^e to it with consequent 
undesirable heating and possibly also drag increabo. The purpose 
of the present report is to treat these problems in somewhat gr-eater 
detail . 

The feared jet processes are caused by the nearr.esE of the wall. 
In order to secure more general and fijndamental data, all special 
wall forms were disregarded and the jet was; meaaiur'ed in the 
proximity of a flat well. This preclu.de d the p?:'ocesses which 
depend on the particular pressure distribution at the wall and 
in the surrounding space. Furtheimore, the work was done on a cold 
jet, principally on account of experimental facility. The extent 
to which fundamental phenomena were suppressed by it must be left 



•■■"Stralilausbreitvng in Wandnahe,'" Zentrale fiir WigsenBchaftlichea 
Berichtsvesisen der Luftfahjrtforschung des Creneralluftzeugmeisters (ZWB) 
BerllivAdlershof, Unterguchungpn i;nd MitteilTaif.-en Nr. 3O57, Dncember 3I, 
19^3. 



MCA TM Ko. 1214 



to future experiments.^ As vai^iable parameters there remain 

the velocity of the Jet, for which as criterion tlie iiean velocity v^ 

in the ezit of the engine model is chosen, and the outer 

flov velocity Vq| and indeed it suggests Itself to once consider 

the difference v^^ - Vq and then the quotient v-ji/Vq as significant. 

Another parameter is the distance a of the exit cone from the 
wall (that ia, the distance of the point of exit closest to the 
wall from the wall) , and lastly the design of the fairing "between 
engine and wall will also play a part. In every case, the thi'ee- 
dimenslonal variation of the jet do-tmstream from the exit must he 
measured. 



II. COKVERGION TO OTHER OPEFiATIM> COUDTl'IOHS 



In view of the multiplicity of potential variations, it is 
desirahle to establish simplifying connections. For practical 
pm-poses it wo^ald he more advantag:eous to he ahle to use easily 
made static tests (without stream flow) and to compute all phuses 
\Tlth stream flow from it. Such a process is described in the 
following: 

It ie assumed that the general state of I'low (v) results, 
in first approximation, from the superposition ox' the stream 
flow (vq) with the Jet flow (v«): 



V = v» + v^ (1) 

This implies that the jot diffusion is to depend only on the 
difference of the velocity in the jet (vp) and outside of the 
Jet (vq), so that the velocity v in the form (v - Vo)/(vji^ - Vq) 
for fixed pai^ticles is independent of the operating condition. 
A cei-tain difficulty is involved in the finding of the location 
of these particles, that is, to pass from the velocity transforma- 
tion (l) to the related transfonaation of the cooixlinates . A 
rectangular system of hody- axes (x, y, z) is used with x in 
the flcfw direction and the time coordinate t, with x = (plane 
of exit) for t = 0. The space coordinates of the paa-ticles 
are functions of the time. Thus for equal time intervals t we 
get a relation between the coordinates x,y,2 of the particle 
in the general flow (v,, ^ o) and the coordinates x*,ySz' o^ 
the flow without streen flow (vg = O) . 

iThe prohlens of model similarity end reproduction of the hot-Jet 
in wind-tunnel tests ere discussed in reference 1. 



IIACA TM No. 121'^ 



It fvirther is assumed that trensverBe floT/s can be diarecarded, 
hence that the velocity has the direction of the x -axis, so that 
y = y* and z = z' . This leaves the connection "between x and t 
and x' and t to ho determined. 

V = — ; v» = — (&) 

dt dt 



the velocity relr-ition (l) then reads 

dx dx* ,„x 

— = + Vo C3J 

dt dt 

which, integrated, gives 

x(t) = x'(t) + v^t {k) 

In this equation t is yet to 'he eliminated and to he replaced 
with the aid of (2) hy neans of the velocity v' = v*(x',y, z), 
which is accessihle to measurement: 

^=l\ v«(xSy,.) ^5) 

In this manner the desired transformation of the cooi-dinates 

,ix'/i 




-.A±ll^_.. (6) 

v»(2:»,y,z) 



'A' 



follovE from (k) , made dimensionlcsv^ with the diameter d of the 
exit nozzle and 'the average velocity v^* = v/^ - Vq in the exit 

nozzle. This transformation states that planes normsJ.- to the x-axis 
are not maintained, hut that according to the velocity distri • 
hution v«(x',y,z) the x displacement for the faster particles is 
less than for the slover ones. In practice '^"'/''"^a' ■'•''^■^^-l'^ ^^ 
measured, the integration carried out,' and the x correspondin/j 
to x' caluclated hy (6) . There the ai-ea cf small velocity would 

cause difficjlties, especially for the points x » 0, ^J j"^ + z'- > d/2, 
since v' vith x -^O must approach zei'o in a certain way in order 
that the integi-al ma^'- exist. Moreover, the mmericsJ. eveluation 
in this ai'ea requires extreme accuracy of measurement. 



MCA TM ITo. 12lij- 



A detailed check of the pi-acticatility of these assumptions " 
was outside the ecope of the present report. A thorougli discussion 
mth consideration of the transverse motions must "be the object 
of a special investigation. For the present, these assiAmptions 
were, after several other simplifications, simply used as "basis 
for the test program. Since the potential coi'e wl-th its high 
dynamic pressures and presuma-hly high temperatures is of particular 
interest in the application, v* = constant was taken 
equal to v/J = "^A " '"'o' Therefore, 

ti ^ ^A/v-o - 1 

This assumption is, of course, justified only for the region around 
the Jet axis up to the dissolution of the potentlsJ. core; however, 
in this ?reglon alone is the assumption of velocity parallel to 
the X-axis satisfied. In view of the mixing motion, it would 
pliysically be more logical if a mean velocity mthin the actual 
mixing zone were regai^dsd as characteristic. The transformation (7)' 
has the advantage of always permitting measurement in planes where 
X = constant. 



III. EXPERIMSriTAX PEOORAM 

In till tests, the difference v_^ - Vq vras kept constant (= 33 m/s) 
The first operating condition with zero stream velocity was: 

State I: Vg = 0; v^v = 33 m/s; v^/vq ="; x = x», 
the second, with comparatively low stream velocity: 

State II: Vq = 11 m/sj v_^ = kh m/sj v^/v^ = ),'-j x = I.33 x' 
and the third, with greater stream velocity: 

State III: Vq = 33 m/s; v;., = 66 m/s; vpjvo -= 2; x = ?x' . 

It was found diaring the measurements that the states I and III 
were inmost cases sufficient for explaining the principal processes. 

The wall distances themselves were limited to a few values, to 
a = d (large dj.stance) and a = d/2( small distance); for comparative 
purposes, data with the jot motor were also measured without a 
wrO-l (a = CO ) . 



MCA TM No. 12114- 



The lining 'heti^en engine and veJ.! was l:ept eapecially slender 
in several caaes, since Kimzo'a tei^ts had shown the impoi'tance of 
adeq.riate ventilation "between jet and vail. As contrast to this 
"good" fa.iiing, a partictilarlj "poor" fairiiif- was used (figi- l) • 
These cowlings all terrd-nated with the exit plan.e of the po-rer xmit. 
In one instance, the good version wae shifted haclnvaj.-d h.y Id and 
cylindrically cut out towai-d the jet, creating a type of "t-annel." 

A model engine with installed blower wtis used. The measvcements, 
made in tuimel No. 2, included total pi^essui-e and etatic pi'essi.u.e 
in y and z direction "ohrougli the jet axit; at various distances 
X train the exit nozzle. 



Vr. EE,5TILTS 



It is foimd that ov<r knowledge of turhulsnt diffusion processes 
is in no way sufficient to explain definitely the Individual 
phenomena. 



1. Without Wall 

Figiu'es 2 to h represent the velocity distributions in the 
jet at vai'iouE <3J.stanccs from the exit nozzle for the tlu'eo 
operating conditions. It portrays the conventlonul . pattern of 
jet diffusion and it must he conceded that the foregoing simplifying 
assiaaptions hold only very rougloly. For the gradual decreare in 
the potential core with increasing:; distance the given transformation 
is practical, hut greater 6.ifferences occux in the transformation 
of the mixing zone, which is in general smaller than the assumption 
stipulates. If the coordinate relation (6) were more accurately 
talcen into account and thus uhe greater values of x ascribed to 
the areas of lower velocity, the ."agreement wo-old be better. Such 
agreement would then be obtained in the boundary zone if the moan 
velocity in the Eilxing zone were used as basis, while the deviations 
in the potential core would become groaoer. It is readily appiaront 
that exact agreement is attained in no instance, hence that other 
pliypicsj. processes must also play a part. Those ai'-e due in peirt 
to the boundrry la;-er on the outer erig;ine svu:'fo,co which is particuJLai'ly 
plain in state III and by which the jet is initially orr-elopod by 
a cushion of retarded air; but with it bhe entire past history of 
the outside flow is involved, so that more general predictions ax'e 
rendered extremely difficult. Moreover, evun for reax<:!on£' of pure 
potential theory, a different jot seems to form with sti-eam flow 
than withoiit it. IThile in state I s *ect angular velocity distribution 
exists in the exit cone and a jet contraction is scarcely noticeable. 



MCA TH No. 12llj- 



the latter is plainly evident in state III as a velocity increase in 
the potential core. This geometrical jet deforiaation could "be 
induced by the shape of the outer contoiir which (in adhering flow) 
gives the velocity at the edge of the nozzle an inwardlj'- directed 
radial component. The jet defonued hy the approach flow gi^es, of 
course, a different "basis for the mlslag of the jot. 

2. Large WeJJ. Distance 

In this instance, the faiiin^iv with its "boimdary layer and the 
"boimdary layer at the wall itself are involvea. For comparison, 
the velocity distribution in the boundaiy layer at the wall in 
the unaffected state was plotted in the same manner as in the 
dia^ams of figure 5. 

In analyzing the i-esults vrith the good faj-rin^ in figures 6 
and 7 the section parallel to the wall (y direction) discloses 
practically no deviations from the corresponding states -.rLthout 
wall. Only the planes normal to the wall (z, direction) mexdfest 
at greater distance fr'OCi the nozzle minor differences which reveal 
a slight travel of the jet toward the wall when no outside flow is 
present. But in state III just the opposite occurs: The ma>:imum 
of the velocity distribution travels perceptibly away from the 
wall. The wal-:o flow of the fairing is scarcely noticeable and 
the boundary layer at the wall also appears to experience no 
substan-oial vat-iation by the flov;-. 

On the poor fairing (figs. 3 and 9) the conditions are 
different. Wliile in state I the jet ntill seems to move a little 
nearer to the wall than with the good fairing, with stream flow 
it ceases to move away from the wall and moves into the dead-air 
region introduced by the fairing. 

To pet some idea of the form of the jet in the vfffiou^ fairings, 
figure 10 represents the lines of eQ.ual velocity in a section normal 
to the flow, as well ae wac possible according to the meaeurements. 
The good as well as the bad fairir^ show- a form no longer axially 
sjTametrical, whic-h, however, is flattened out at the wail side 
in the first case and ovally puJ.led tovrard the wall in the other. 
The movement of the velocity maxim'om in .iiffei-ent directions is 
plainly visible. According to this, it might be suspected that 
the good ventilation of the space between en£;lnc and wall with the 
good fairing forms a definite air cushion which pushes the jet 
ai-.^ay from the wall. This concept is supported by the conditions 
in a horizontal section tlirough the jet xn figui-'c 11. 



MCA TM Nc. 12lil- 



However, in spite of thei30 dj-ssimilai^ities, the effects are 
cciiip8j.'atively small. In the projc.imity of a flat wa].l, the 
possibility/ of a ventilation l"roni the sides is so great as to 
preclude the existence of jet adherence even vith an extremely 
poor fairing. 



3. Short-Well Distance 

One noteworthy fact ir; that the aforementioned processes 
are repeated with the short wall distance, hence ai^e not limited 
to the comparativelj'" large distance frcaE the wail. As with tlie 
pood fairing, there is a slirht movement towai'd the wall in 
the absence of stream flow ana a movement awaj'' from iz with 
increasing stream flair (fige. 12 end I3) . 

The fairing with tiinnel extending ba'jkwai-d beyond the afteibod;}'- 
of the engine \mit is of practical interest for the reason that 
in many cases it Is the only way to obtain a sufficiently elongated 
fona. This fairing likewise exhibits no markedly unfavorable 
behavior. The jet naturall;^ adheres in this case at the tunnel 
(figB. Ik and i;;) • This tunnel surface was therefore to have 
no projected area in the flight direction for reasons of i'esistance. 
Since, however, the tunnel must be adapted to the form of the jet, 
and this is not known at once for the different cnginoi uirits, 
difficulties may arise, so that, if at all possible, such a tunnel 
fairing should be avoided. 

It is perhaps not immediately comprehensible whj'" in these 
measui'ements only these fevr generalized types of fairings were 
investigated axxd the form of the fairing' not fui'ther varied, 
to est-ablish, for example, which form could be still designated 
as good. According to the cited results, however, the solution 
of such a problem does not appear possible at once, since it was 
seen that geometrical conditions such as the form 01 the afterbody 
of the engine iinit or the past history of the outer flow ha/e some 
effect on the phenomena, so that a separation of these pi'oblr.ms 
from the others for the installation of given conditions seems 
hardly correct, and the Reynolds number and the tempe.rutui"'e 
conditions woxild then also have to be teicen in'iio accoimt: Hence 
the limitation to basic experiments. That the conditions in an 
installed jet -propulsion urdt are similar in the fundamental 
phenomena is shotm by the wind-tunnel tests on an auxiliary 
ti;arbojet niit model mo-jnt^-d below the fuselage on the Heinkel J19 
(reforence 2) . So, in order to be absolutely' certain about the 
jet diffusion for a spocific design, a test on the total model 



WACA TM Wo. 1214 



is probably unavoidable, and judged by past experiences, a water-channel 
test is best suited for this purpose. 



Translation by J. Vanier 
National Advisory Committee 
for Aeronautics 



PEFERETJCES 



1. Brennecke, H. : Messungen an dem Modell einer Strahlantriebsgondel. 

Forschungsbericht Nr. 17^3 , 19'<-3' 

2. Bauerle, H. and Hildenbrand, H. : Widerstands und Schubanderun3 

bei nachtraglichen Anbavi eines TL—Triebwerkes unter den Eujnpf 
der He i:^19. Untersuchungen und Mitteilungen Wr. 30i)-l, 19i4-3. 

3. Kuchemann, D. and Weber, J.: Uber die Stroaiung an ringformigen 

Verkleidungen. XI. Mitteilung: Wandnahe Einlaufe. Untersuchungen 
und Mitteilungen Nr. 3O5I, 19^+3. 



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Lines of equal velocity In jet 
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Exit 



IT /Vo =0.9 




Wall 



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UNIVERSITY OF FLORIDA 
DOCUMENTS DEPARTMENT 

GAINESVILLE. FL 32611-7011 USA 



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UNIVERSITY OF FLOFIIDA 



3 1262 08106 443 7 



UNIVERSITY OF FLORIDA 
DC TMEIMT 

4 SCIENCE LIBRAfW 

K^ .)11 

''-' cn '^'^61 1-7011 USA